[R] fft: characteristic function to distribution

[Jindan Zhou]

Hello members!

This question had been posted by Thomas Steiner in May, but I couldn't
locate any followups thereafter, see:
https://stat.ethz.ch/pipermail/r-help/2008-May/161483.html

I want to raise up this question in a (hopefully) even simpler way:

Given a random variable X, it's characteristic function and density
function forms a Fourier pair. In the case of standard normal
distribution, the characteristic function has the form:
char=exp(-(t^2)/2)

Is it possible to use fft function in R to recover the density (or
cumulative) function of the standard normal distribution? If yes, can
someone demonstrate with code?

Thanks in advance for the help! I am working on a financial project
and really need an working example to understand the whole picture.

Jindan